04423nam a22005415i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001600172072001700188072002300205082001400228100003100242245009300273264004200366300004600408336002600454337002600480338003600506347002400542490004400566505031300610520232100923650001703244650002303261650002203284650002503306650002103331650002503352650001703377650002503394650002203419650005403441650004103495650003203536650002103568710003403589773002003623776003603643830004403679856004803723912001403771999001903785952007703804978-0-8176-4678-3DE-He21320180115171438.0cr nn 008mamaa100301s2008 xxu| s |||| 0|eng d a97808176467839978-0-8176-4678-37 a10.1007/978-0-8176-4678-32doi 4aQA319-329.9 7aPBKF2bicssc 7aMAT0370002bisacsh04a515.72231 aChristensen, Ole.eauthor.10aFrames and Basesh[electronic resource] :bAn Introductory Course /cby Ole Christensen. 1aBoston :bBirkhàˆuser Boston,c2008. aXVIII, 313 p. 14 illus.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aApplied and Numerical Harmonic Analysis0 aFrames in Finite-dimensional Inner Product Spaces -- Infinite-dimensional Vector Spaces and Sequences -- Bases -- Bases and their Limitations -- Frames in Hilbert Spaces -- B-splines -- Frames of Translates -- Shift-Invariant Systems -- Gabor Frames in L(R) -- Gabor Frames in l(Z) -- Wavelet Frames in L(R). aDuring the last several years, frames have become increasingly popular; they have appeared in a large number of applications, and several concrete constructions of frames of various types have been presented. Most of these constructions were based on quite direct methods rather than the classical sufficient conditions for obtaining a frame. Consequently, there is a need for an updated book on frames, which moves the focus from the classical approach to a more constructive one. Based on a streamlined presentation of the author's previous work, An Introduction to Frames and Riesz Bases, this new textbook fills a gap in the literature, developing frame theory as part of a dialogue between mathematicians and engineers. Newly added sections on applications will help mathematically oriented readers to see where frames are used in practice and engineers to discover the mathematical background for applications in their field. Key features and topics: * Results presented in an accessible way for graduate students, pure and applied mathematicians as well as engineers. * An introductory chapter provides basic results in finite-dimensional vector spaces, enabling readers with a basic knowledge of linear algebra to understand the idea behind frames without the technical complications in infinite-dimensional spaces. * Extensive exercises for use in theoretical graduate courses on bases and frames, or applications-oriented courses focusing on either Gabor analysis or wavelets. * Detailed description of frames with full proofs, an examination of the relationship between frames and Riesz bases, and a discussion of various ways to construct frames. * Content split naturally into two parts: The first part describes the theory on an abstract level, whereas the second part deals with explicit constructions of frames with applications and connections to time-frequency analysis, Gabor analysis, and wavelets. Frames and Bases: An Introductory Course will be an excellent textbook for graduate students as well as a good reference for researchers working in pure and applied mathematics, mathematical physics, and engineering. Practitioners working in digital signal processing who wish to understand the theory behind many modern signal processing tools may also find the book a useful self-study resource. 0aMathematics. 0aHarmonic analysis. 0aFourier analysis. 0aFunctional analysis. 0aOperator theory. 0aMathematical models.14aMathematics.24aFunctional Analysis.24aFourier Analysis.24aMathematical Modeling and Industrial Mathematics.24aSignal, Image and Speech Processing.24aAbstract Harmonic Analysis.24aOperator Theory.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9780817646776 0aApplied and Numerical Harmonic Analysis40uhttp://dx.doi.org/10.1007/978-0-8176-4678-3 aZDB-2-SMA c369975d369975 001040708EBookaelibbelibd2018-01-15r2018-01-15w2018-01-15yEBOOK